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Basic NMR Concepts:
A Guide for the Modern Laboratory
Description:
This handout is designed to furnish you with a basic understanding of Nuclear Magnetic
Resonance (NMR) Spectroscopy. The concepts implicit and fundamental to the operation
of a modern NMR spectrometer, with generic illustrations where appropriate, will be
described. It can be read without having to be in front of the spectrometer itself. Some
basic understanding of NMR spectroscopy is assumed.
Table of Contents:
Basic NMR Concepts.
I. Introduction
II. Basics of FT-NMR: Six critical parameters.
III. Applications of FT-NMR
1) Shimming, line widths, and line shapes
2) Signal-to-noise measurements
3) Integration
4) Homonuclear decoupling
5)
13
C-{1H} spectra
6)
13
C-{1H} DEPT spectra
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Introduction
Nuclear Magnetic Resonance (NMR) is a powerful relatively non-selective
analytical tool, which enables you to ascertain molecular structure including relative
configuration, relative and absolute concentrations, and even intermolecular interactions.
Once challenging and specialized NMR techniques have become routine. NMR is indeed
an indispensable tool for the modern scientist. Chemists, with little knowledge of NMR,
are now able to obtain 2- or even 3-dimensional spectra with a few clicks of a button.
Care must be taken, however, when using such ‘black box’ approaches. While the
standard parameters used in the set-up macros for experiments might be adequate for one
sample, NMR system, or hardware configuration, they may be very wrong for another. A
single incorrectly set parameter can mean the difference between getting an accurate,
realistic spectrum and getting a meaningless result, or even worse, damaging equipment
that often costs several hundreds of thousands of dollars. A basic understanding of a few
key aspects of NMR spectroscopy can ensure that you obtain the best results possible.
This guide is intended to highlight the most pertinent aspects of practical NMR
spectroscopy. It is not meant to replace any formal training of the theory of NMR.
"Modern pulse NMR is performed exclusively in the Fourier Transform mode. Of
course it is useful to appreciate the advantages of the transform, and particularly the
spectacular results that can be achieved by applying it in more than one dimension, but it
is also essential to understand the limitations imposed by digital signal analysis. The
sampling of signals, and their manipulation by computer, often limit the accuracy of
various measurements of frequency and amplitude, and may even prevent the detection of
signals altogether in certain cases. These are not difficult matters to understand, but they
often seem rather abstract to newcomers to FT NMR. Even if you do not intend to operate
a spectrometer, it is irresponsible not to acquire some familiarity with the interaction
between parameters such as acquisition time and resolution, or repetition rate,
relaxation times and signal intensity. Many errors in the use of modern NMR arise
because of a lack of understanding of its limitations."
From A.E. Derome, Modem NMR Techniques for Chemistry Research (1987)
Basics of FT NMR- Six Critical Parameters
This section will give you enough information about FT-NMR experiments to
avoid the most common errors. We will cover the most important parameters that affect
any spectrum you may collect using an FT-NMR spectrometer. These are:
1. Spectrometer Frequency [sfrq]
2. Pulse Width [pw]
3. Acquisition Time [at]
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4. Number of Points [np]
5. Sweep Width [sw]
6. Recycle Delay [d1]
[The blue letters in square brackets following the parameter represent the mnemonic used
(the command), on all Varian spectrometers in the VNMR software package. The
parameters are discussed in more detail below.]
The most basic and common pulse sequence you will encounter is the ‘1-PULSE’
FT-NMR experiment (e.g. seqfil = ‘s2pul’ in VNMR), which is the sequence used for
routine 1H and 13C acquisitions. It can be represented as shown in Figure 1. In a typical
NMR acquisition, this pulse sequence will be repeated many times in order to improve
the signal-to-noise ratio (S/N), which increases with the square root of the number of
transients that are averaged together (nt). The user can independently set each of the
parameters shown in Figure 1. Knowledge of their purpose and function will help you
obtain quality NMR spectra. On Varian spectrometers, you can view the current pulse
sequence by typing ‘dps’.
Pulse Width (pw)
Recycle Delay (d1)
Acquisition Time (at)
Figure 1. Schematic representation of one pass of a simple ‘1-PULSE’ pulse sequence.
1. Spectrometer Frequency [sfrq]:
It is called a “1-PULSE” experiment because one radio frequency (Rf) pulse (pw)
is applied per cycle. The Rf pulse excites the nuclei, which then emit Rf during the
acquisition time, giving rise to an NMR signal in the form of an exponentially decaying
sine wave, termed free-induction decay (FID). The Rf pulse has a characteristic
frequency, called the spectrometer frequency (sfrq), which is dependent upon the nucleus
you wish to observe and the magnetic field strength of the spectrometer. NMR
spectrometers are generally named for the frequency at which hydrogen atoms resonate.
Thus, a Varian INOVA 500 will cause hydrogen atoms to resonate at approximately 500
MHz. The precise spectrometer frequency defines the exact center of the NMR spectrum
you measure.
An Rf pulse that excites spins at only one exact frequency is not desirable because
the NMR frequencies are spread out over a range of frequencies called the range of
chemical shifts (corresponding to ~10 ppm of the applied magnetic field for 1H and ~250
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ppm for 13C). Luckily, the short pulse lengths used in FT-NMR (e.g. ~10 µs) causes the
Rf power to be distributed over a corresponding frequency spread (~1/pw, or 1/0.00001
seconds = ~100,000 Hz) due to the Heisenberg Uncertainty Principle. As you shorten the
pulse length and increase power, uncertainty in the frequency results in a larger field of
excitation (frequency range of power deposition). A longer, lower power pulse will have
less frequency spread and can be used for frequency selective excitation or saturation.
2. Pulse width [pw]:
Prior to applying an Rf pulse, the majority of nuclear spins are aligned parallel to
the static magnetic field (B0). The axis of alignment is typically designated the Z-axis
and the bulk magnetization is shown as a bold arrow (Figure 2, left side). Application of
a short Rf pulse at the appropriate frequency will rotate the bulk magnetization by a
specific angle. Pulses are generally described by this angle of rotation (also called flip
angle). The angle of rotation is dependent on the intensity of the pulse (tpwr) and the
width of the pulse (pw). The maximum measurable signal can be recorded following a
90º rotation or pulse. Thus, a 90º pulse width is defined as the amount of time the pulse
of Rf energy is applied to the particular sample (90º is not 90º for all samples!) in order to
flip the bulk magnetization from the Z-axis precisely into the X-Y plane, i.e., the
condition shown in Figure 2A. For example, the 90º pulse width for 1H NMR
experiments might be about 8 µs on the Varian Inova 500. It is often very useful to talk
about the strength of the oscillating magnetic field associated with the Rf pulse in terms
of the rotation frequency (rather than the time required to rotate the bulk magentization
90º). For example, if it takes 8 µs to rotate 90º, then using the same Rf intensity it will
take 4*8µs = 32 µs to rotate 360º. The intensity of the Rf field can then be described as a
magnetic field that causes the magnetization to rotate at a rate of 1/32 µs, or at 31,250 Hz
(31.25 KHz). We call this magnetic field the B1 field, analogous to our description of the
main static magnetic field (B0). (Note: a 300, 400, or 500 MHz static B0 field is roughly
10,000-20,000 times stronger than a typical oscillating B1 field that comes from the Rf
pulse). The importance of learning this convention will become strongly apparent when
you setup a homonuclear decoupling or nOe experiments, or perhaps a two-dimensional
TOCSY experiment.
The pulse width is entered in microseconds by typing pw=desired value in
microseconds. The exact value is dependent upon the sample (nucleus, solvent, etc.) as
well as the instrument (probe, etc.). Methods for measuring the pulse width will be
discussed in another handout and are, for the most part, not required until you attempt
advanced experiments. For routine one-dimensional survey experiments, most users use a
25 - 45º pulse for their data collection (Figure 2B). The reasons for this are discussed
under recycle delay (d1).
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Z
Z
900
A)
Y
PW= 10 µs (900)
Y
B0
X
X
Z
Z
450
B)
Y
PW= 5 µs (450 )
Y
B0
X
X
Figure 2. The bulk nuclear spin magnetization (bold arrow) for an NMR sample placed
in a magnetic field aligned along the Z-axis before and after application of a pulse.
3. Acquisition time (at):
Thus far, we have sent an Rf pulse through the sample and flipped the bulk
magnetization by a specific angle. The nuclear spins are no longer at equilibrium and
will eventually return to equilibrium along the Z-axis. One of the most extraordinary
aspects of NMR is that the relaxation back to equilibrium takes from 106-1012 times
longer than many other spectroscopies that you routinely utilize! In Figure 1, the
decaying sine wave represents this process of Free Induction Decay (FID), which is a plot
of emitted radio intensity as a function of time. The time it takes to acquire the FID is
called the acquisition time and is set by the parameter ‘at’. For most nuclei of interest to
chemists, relaxation times are within the range of 10-1 to 10 seconds. One of the most
important concepts that chemists should learn is that routine matching of the acquisition
time to the full decay time of the FID is a primary goal in recording quality NMR data. A
natural inclination might be to just increase the acquisition time to maximize the amount
of signal that is acquired (up to some “safe” limit). However, increasing the acquisition
time is only advantageous up to a point. Moreover, it will be detrimental if extended too
far. Care and forethought should be taken when adjusting ‘at’: too long and you will
acquire noise unnecessarily; too short and extraneous wiggles will show up at the base of
the peaks.
4. Number of points (np):
The tiny analog signal emitted from the sample (in microvolts) is amplified,
mixed, filtered, and attenuated prior to digitization, which is required for further
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computer processing. The ADC (analog-to-digital converter) converts the analog FID
into a series of discrete points along the FID signal envelope. This is the number of points
(np). In general, the more points used to define the FID, the higher resolution. The
number of points (np),
FT
sfrq = 500.075 MHz
Figure 3. Fourier transform of the FID for estrone acquired at 500 MHz. Note: the
spectrometer frequency you use, in general, will not be exactly 500 MHz.
spectral width (sw), and acquisition time (at) are interrelated. Changing one of these
parameters will affect the other two (see below).
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5. Spectral Width (sw):
While the FID contains all the requisite information we desire, it is in a form that
we cannot readily interpret. Fourier transforming the time-domain (seconds) FID
(commonly referred to as FT or FFT for Fast Fourier Transform) will produce a
frequency domain (seconds-1) spectrum with the familiar peak shapes and intensities, as
shown in Figure 3. The frequency domain spectrum has two important parameters
associated with it; the spectrometer frequency (sfrq), discussed earlier, and the spectral
width (often times erroneously called the sweep width)(referred to as sw - see Figure 4).
It is important to remember that the spectral width in ppm is independent of the
spectrometer operating frequency; however, since the number of Hz per ppm is
dependent on the spectrometer operating frequency, the spectral width in Hz will change
depending upon the spectrometer used. For example, at a spectrometer frequency of
300 MHz, a spectral width of 3000 Hz is needed to measure a 10 ppm frequency range,
since each ppm contains 300 Hz (10 ppm x 300 Hz/ppm = 3000 Hz). At a spectrometer
frequency of 500 MHz, a spectral width of 5000 Hz is needed to measure 10 ppm (10
ppm x 500 Hz/ppm).
500 MHz
300 MHz
10 ppm
0 ppm
10 ppm
0 ppm
3000 Hz
0 Hz
5000 Hz
0 Hz
Figure 4. The spectral width in ppm and Hertz at different spectrometer frequencies.
Note the difference in the spectral width in Hertz for the two spectrometers.
The sweep width (sw), number of points (np), and the acquisition time (at) are
related by the following equations:
np
2sw
(1)
1 2sw
=
at
np
(2)
at =
and
€
res =
where ‘res’ refers to the digital resolution of the spectrum. The digital resolution is in
units of Hz/point, and the rule-of-thumb is that the digital resolution (in Hertz) should be
€
less than one half the natural peak width at half-height. This ensures that each peak is
described by at least 3 points. For example, if your peak width at half-height is 0.5 Hz,
the digital resolution should be less than 0.25 Hz. Therefore, if your spectrometer
frequency is 500 MHz, your total spectral width is 5000 Hz (10 ppm) and your required
digital resolution (res) is 0.25 Hz/point, rearranging equation 2 gives you the minimum
number of points required for adequate digital resolution:
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np =
2sw
= 40,000 points
res
(3)
Since the computer works most efficiently if the number of points is a power of 2,
the closest larger power of 2 would automatically be used, which, in this case, is 65,536
€
points. The spectral width, number of points, and acquisition time can be specified when
operating the spectrometer, usually by typing the appropriate mnemonic followed by an
equals sign and the numeric value (e.g. np=64000). The spectrometer will set the units
automatically. Generally, Varian’s automatically change the number of points according
to equation 2 if the acquisition time or sweep width are changed.
6. Recycle delay (d1):
On Varian’s this delay time is named d1 and appears at the beginning of the pulse
sequence (see Figure 1). In practice, this delay should be thought of as coming after the
acquisition time. It is an important parameter and plays a vital role in obtaining accurate
integration. After the Rf pulse, the nuclear spins do not instantly return approach
equilibrium; rather, they each relax according to a time constant called T1 (longitudinal
relaxation time, which parameterizes any approximation of the time necessary for the
magnetization to approach the Z-axis). Individual T1 time constants are dependent on
many factors including nuclear environment, temperature, and solvent. T1’s for carbon
atoms are typically much longer than T1’s for hydrogen atoms. Since each nucleus in a
molecule is immersed in a different magnetic environment, their T1’s will not be the
same. Not allowing enough time for relaxation between pulses will cause varied
attenuation of the signals and inaccurate integration (see Integration Section for more
details). When a 90° pulse is used to excite the spins (Figure 2A), a total time (TT)
between pulses of 5xT1 is necessary in order to have nearly complete relaxation. (Zmagnetization = (1 – e-(elapsed time/T1)), where 1 – e-5 = ~ .99326). If a pulse width less than
90° is used, the total time can be proportionally less, and intensity distortions due to
differential relaxation effects can be minimized. This is one reason why the standard
pulse width for 1D 1H NMR experiments are in the range of 25 - 45º.
The total time between measured transients is given by the following equation,
where TT is the total time and d1 is the recycle delay: TT = pw + at + d1. Since the
pulse width is in microseconds while the acquisition time and recycle delay are in
seconds, the pulse width can usually be ignored, leaving us with the equation:
TT = at + d1
(4)
The optimum recycle delay can be computed by rearranging the equation to give
€
d1 = TT − at
As an example of the above, if your longest T1 is 600 msec, then the total time (where
€
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(5)
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TT=5x T1) must be at least 3 seconds, to completely avoid relaxation based distortions of
signal intensity.
Take Home Lesson
These six parameters provide the foundation on which all NMR experiments are
built. Appreciation of them will go far in the correct acquisition and interpretation of
your NMR spectra, thus, saving precious time and effort. This not only applies to simple
1-PULSE experiments, but also is equally important in 2-D and 3-D NMR spectroscopy.
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Applications of FT-NMR
1. CHCl3 Peak Width at Half Height (LW1/2).
The purpose of this section is to acquaint you with proper peak shape and the
problems that are caused by improper shimming. NMR peaks have a shape that is called
Lorentzian. A Lorentzian line can be expressed mathematically and has three
parameters: amplitude [A], width at half height in Hz [LW1/2] and position, in Hz [X0].
An example of a Lorentzian line with LW1/2 = 0.25 Hz is shown below, in Figure 5.
Xo
Y=
A(LW1/ 2 ) 2
(LW1/ 2 ) 2 + 4(X 0 − X) 2
A
LW1/2
A = Amplitude
LW1/2 = Peak width at half height, in Hz
X 0 = Peak position, in Hz
-5
-3
-1
1
Hertz
3
5
€
Figure 5. Lorentzian line with LW1/2=0.25 Hz.
The minimum obtainable peak width at half-height is directly related to the
resolution of an instrument; i.e., how close two peaks can be and still be distinguishable.
Resolution is usually measured using o-dichlorobenzene, which has very narrow lines in
its 1H NMR spectrum. The manufacturers' resolution specification is usually 0.20 Hz,
although peak widths of less than 0.10 Hz are obtainable by an expert shimmer.
Manufacturers of NMR instruments, however, have traditionally separated the resolution
specification from the lineshape specification. Line shapes for 1H NMR spectra are
usually specified using CHCl3 and the specifications are stated in terms of the peak width
at half-height, 0.55%, and 0.11 % height of the CHCl3 peak. The latter two percentages
are chosen because they are the height of the l3C satellites of the CHCl3 line and one-fifth
this height. These values are meaningful only when compared with the half-height width.
From the mathematical equation for a Lorentzian line (see Figure 5), the line width at
0.55% height is calculated to be 13.5 times LW1/2, while the line width at 0.11 % height
is calculated to be 30 times the LW1/2. So, if the peak width at half-height is 0.30 Hz, the
calculated values are 4.0 Hz at 0.55% and 9.0 Hz at 0.11 %. For comparison, the
manufacturer's specifications are 10-15 Hz and 20-30 Hz at 0.55% height and 0.11 %
height, respectively. These values are larger than the theoretical values because the line
widths at 0.55% and 0.11 % height are very sensitive to shimming. Other factors that
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influence line shape include the quality of the NMR tube, sample spinning, sample
concentration, dissolved oxygen, and paramagnetic impurities. The latter three will lead
to an overall broadening of the lines.
Shimming:
The term ‘shimming a magnet’ is a piece of NMR jargon that harks back to the
early days of NMR spectroscopy. Originally, permanent magnets were used to provide
the external magnetic field. To obtain the most homogenous field across the sample, the
pole faces of the magnet had to be perfectly aligned, and to accomplish this, small pieces
of wood, or ‘shims’, were hammered into the magnet support, so as to physically move
the poles relative to each other. Luckily, nowadays you will not be required to bring
hammer and wooden shims to the spectrometer. Shimming is accomplished by changing
the applied current for a set of coils surrounding the probe. This applied current will
create small magnetic fields in the region of your sample that will either enhance or
oppose the static magnetic field. Your goal will be to adjust these coil fields by a series of
mouse clicks to obtain the most homogeneous magnetic field across your sample, which
is usually observed as an increase in the lock signal.
It is important for you to have a basic understanding of line shape so you can
judge when: (1) your shimming is off, and (2) you need to spend more time shimming
your sample. The best way to avoid problems is to establish a procedure, such as the one
detailed below.
I.
Always load a shim file that matches the current probe (e.g. probe = ‘as’ )
when you sit down at the instrument. You should never assume the
previous user left the instrument with a standard shim file loaded. Without
reloading standard shims, you will have to start where the last person
stopped - and that might include someone who shimmed for a short
sample, a bad tube, a viscous sample, etc.
II.
Be aware of lock parameters, especially if you only shim on the lock
display (as most novice users will). Establish lock transmitter power and
gain levels that work for most of your samples. If you encounter a sample
that seems to require an unusually high power or gain setting, there is a
problem with your sample and/or the instrument, and shimming on the
lock level may be difficult or impossible.
III.
Shimming problems are confirmed only if the problem is visible on every
peak in your spectrum. If, for example, only one peak is doubled, the
problem is sample related, and can't be shimmed away. Remember,
anomalies close to the base of intense single lines may not be visible on
less intense peaks unless the vertical scale is increased.
IV.
Establish a shimming method. Shimming is an ‘art form’ that requires
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patience and practice. You should always approach shimming with some
method that works for you to give acceptable results. Example: load a
shim file; adjust the lock level to a maximum with Z1, then Z2, then Z1,
then Z3, and then Z1.
V.
Spinning side bands should always be below 2%. If spinning side bands
are above 2%, turn off the spinner air, optimize the X and Y shims, then
turn the spinner air back on and re-optimize Z1, Z2, and Z3. If this does not
solve the problem, consider transferring your sample to another tube.
Knowledge of correct line shape can help you correct problems such as those
shown in Figure 6. Although the peak in Figure 6b may have a line width at half-height
that is less than 0.50 Hz, it is obviously poorly shimmed. You should never accept a
poorly shimmed line shape such as is shown in Figure 6b, where a single line is expected.
On the pages that follow are some line shape defects and the shims that should be
adjusted to correct the problem. You will also notice that the FID will show the problem
as well, but may not be as easy to diagnose. In general, odd-order longitudinal shims (Zl,
Z3, Z5) affect the line shape symmetrically while even-order longitudinal shims (Z2, Z4)
cause a non-symmetrical line shape. The higher the order (Z4 is higher order than Z2), the
lower (closer to the base of the peaks) the problem is observed.
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Figure 6. From G. Chmurny and D. Hoult, “The ancient and honorable art of shimming.”
Concepts in Magnetic Resonance, 1990, 2, 131-149.
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Shimming Take Home Lesson
The ‘art’ of shimming resides in the fact that there is no single set of rules that
work for every sample, spectrometer, person, or even time of year. Personal experience
is the best and, frankly, the only way to master shimming. That being said, knowledge of
correct and incorrect line shapes will allow you to decide quickly whether your sample is
correctly shimmed. You will have to decide whether the return (a better line shape) is
worth the time spent achieving that line shape.
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Signal-to-Noise Measurement
The signal-to-noise measurement, or S/N, is an important criterion for accurate
integrations, and is also one of the best ways to determine the sensitivity of a NMR
spectrometer. In general, a higher S/N specification means that the instrument is more
sensitive. It is also useful in roughly determining the time requirement for an experiment.
Standard S/N measurements for 1H spectra are always determined using a sample of 0.1
% ethylbenzene in CDCl3 (ETB). A typical result for the Varian Inova 500 is 200:1 using
the 5mm probe. It is important that the spectrum be acquired under the following
standard conditions:
1. Use a 90 pulse.
2. Line Broadening of 1.0 Hz.
3. Spectral Width of 15 to 5 ppm.
4. A sufficient relaxation delay (at least 5xT1).
5. A sufficient digital resolution (less than 0.5 Hz/point).
6. One transient.
Optimum signal-to-noise for any sample is defined as that which occurs when
using a line-broadening equal to the peak width at half height. When this line broadening
is applied, the peak width at half-height doubles, i.e., it is the sum of the natural peak
width at one-half height plus the line broadening applied. The equation used for
calculating S/N is:
S /N =
2.5A
N pp
(5)
(where A = height of the chosen peak and Npp = peak-to-peak noise).
€
Peak-to-peak noise means exactly that - a measurement from the most positive to
the most negative positions for the noise. As shown below, the widest differences are
used for the measurement.
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The distance between the two horizontal lines, above, in mm, is the Npp value to
be used in equation (5). Choice of a noise region must be consistently applied for
standard samples, and for 0.1 % ethylbenzene (ETB), use 5 to 3.5 ppm. S/N measurement
is an automated process and only requires choice of the appropriate window, placement
of the cursors, and typing the correct command (‘dsn’ on Varian instruments).
The signal-to-noise of a given signal increases as the square root of the number of
acquisitions; therefore, to double the signal-to-noise you must take four times as many
acquisitions. When using a concentrated sample such as 5% (w/v) menthol for 13C, or
when measuring routine 1H survey spectra, the number of scans is often quite small, so
the point discussed above may not seem important. However, suppose you are in the
following situation: you have only a few mg of research sample, and after measuring a
13
C spectrum for 2 hours, you get peaks with an S/N of only 5:1. Since the peaks are
barely visible above the noise (and you may have missed signals for any quaternary
carbon atoms), you want to re-collect the spectrum to get an S/N of 50:1, a value more
typical for 13C NMR. Unfortunately, this will take 10 * l0 * 2 = 200 hours!
S/N Take Home Lesson
At some point, you may measure a spectrum and wonder why the signals are so
weak. The majority of the time, the problem is not with the spectrometer, but with your
sample. You can test this quickly by taking a spectrum of a standard such as ETB or
menthol. In this way, you can save yourself needless frustration by identifying problems
that are due to a bad sample. It is always a good practice to measure the spectrum of a
standard, well-characterized compound before that of your unknown.
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Integration
The purpose of this section of the handout is to show you how to obtain accurate
integrals. The spectrum of 0.1 % ethylbenzene in CD2C12 is given in Figure 7. CDCl3 is
not used in this case because the solvent peak overlaps with the phenyl region and
complicates integration. If we assign an integral of 3.00 to the CH3 triplet, then the
phenyl region integrates to 4.12 protons, while the CH2 quartet integrates to 1.93 protons.
Thus, the integral for the phenyl protons is 15.6% too small, while the integral for the
CH2 quartet is off by only 3.5%. The 14.2% error for the phenyl protons is not due to
spectrometer error, it is because we have chosen parameters for acquiring the spectrum
that guarantee we will get inaccurate integrals.
Figure 7. 1H NMR spectrum of 0.1% ethylbenzene in CD2Cl2 taken on a Varian INOVA
500 MHz spectrometer with no recycle delay (nt=4, d1=0). The longest T1 for this
sample was measured at 12 seconds.
The accuracy of the integrals obtained for most routine spectra is usually about
10-20%. This accuracy is sometimes sufficient, especially if you already know what the
compound is. However, this accuracy is usually not adequate to determine the exact
number of hydrogen atoms contributing to a given peak, nor is it sufficient for
quantitative applications (such as kinetics experiments or assays of product mixtures)
where one demands an accuracy of 1-2%. For example, 20% accuracy is not sufficient to
decide whether two peaks have a relative ratio of 1:3 or 1:4. Obtaining 1-2% accuracy
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can be achieved but you need to be aware of the factors that affect integrations. These are
as follows:
I.
There should be no nuclear Overhauser effect contributions or any other
effects that selectively enhance certain peaks. This is a problem only with X
nuclei such as 13C and will be dealt with in section 4.
II.
No peaks should be close to the ends of the spectrum. The spectral width
should be large enough such that no peak is within 10% of the ends of the
spectrum. This is because the spectrometer uses filters to filter out frequencies
that are outside the spectral width. Unfortunately, the filters also tend to
decrease the intensities of peaks near the ends of the spectrum. For example,
at 500 MHz, if two peaks are separated by 7 ppm, a spectral width of at least
3500 Hz is sufficient to get both peaks in the same spectrum and prevent
foldovers. However, to avoid distortion of the integral intensities because of
filter effects, the spectral width should be set 10% larger on each side, 350 Hz,
giving a total spectral width of about 4200 Hz (8.4ppm). Thus, you should be
prepared to make the spectral width larger if necessary. When in doubt, it is
best to be conservative. Hence if the peaks are separated by 3500 Hz, one can
easily set the spectral width to 6000 – 8000 Hz. With modern spectrometers,
this change puts an insignificant burden on the hardware.
III.
The recycle time + the acquisition time = total time (TT) should be at least
five Tl 's. Data should be collected under conditions which ensure that all the
nuclei can fully relax before the next FID is taken. The most challenging
aspect of this criteria arises from three experimental variables. First, the
acquisition time (at), should always match the sample. If the FID “rings”
down quickly, a short value of at is fine. However, if the FID rings down
slowly, then the value of at should be long enough such that it exceeds the last
possible evidence of signal by about 50%. (You should routinely examine the
time it takes the FID to ring down using the df (display FID) command). Next
you need to consider how long T1 may be with respect to the value of at.
Note: when using a relatively long value at, with T1 values that are not very
long, means that you can use a relatively modest d1 value and still enjoy
nearly complete relaxation before the next pulse occurs. However, this is
rarely the case. Hence, in contradistinction, in the case of 0.1 % ethylbenzene
in CD2C12, where the longest Tl of interest is 9.8 sec (phenyl hydrogen
atoms), so the TT when using a 90º pulse width should be 49 seconds. Even
for a relatively long value of at (e.g. up to 6 – 10 seconds), a very long value
of d1 will be necessary to obtain accurate integrals.
IV.
The spectrum should have a S/N of at least 250:1 for the smallest peak to be
integrated. Usually if you cannot see any baseline noise, you probably have
close to the required S/N for accurate integrals.
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V.
The baseline should be flat. Distortion due to phase problems should be
corrected. Baseline distortion due to non-optimum parameter selection that
causes a baseline roll will not be discussed here. See lab staff for help if you
suspect this problem. (Note: parameters in this group include gain, sw, fb,
rof2, alfa, lp and rp.)
VI.
The peaks need to be sufficiently digitized, as discussed earlier in this
handout. If the linewidth at half-height is 1 Hz, you need a digital resolution
of less than 0.5 Hz.
VII.
The same area should be included or excluded for all peaks. For example, all
peak integrals should be measured +/- 5 Hz around each peak, not +/- 20 Hz
around one peak, +/- 10 Hz around a second peak, etc. Spinning sidebands are
included in this category, and should consistently be either included or
excluded.
Figure 8. 1H NMR spectrum of 0.1% ethylbenzene in CD2Cl2 taken on a Varian INOVA
500 MHz spectrometer with a recycle delay of 60 seconds (nt=4, d1=60). The longest T1
for this sample was measured at 12 seconds.
With these points in mind, let’s take the 1H spectrum of ethylbenzene again. The
major factor for poor integration in Figure 7 was the difference in T1’s for the aromatic
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protons (~12 seconds) and the aliphatic protons (~7 seconds). With no recycle delay,
there was not enough time to allow for complete relaxation. If we allow for complete
relaxation by setting d1 large enough, say 60 seconds, then integration becomes accurate
as shown in Figure 8 with only a 0.2% error of the aromatic protons.
Integration Take Home Lesson
Taken from Derome (p. 172)
“The moral of this section is that there are numerous contributions to the error in
a quantitative measurement made by FT NMR, and while each of them may be reduced to
1% or so in a practical fashion, the combined error is still likely to be significant. I am
always skeptical of measurements purporting to be accurate to better than a few percent
overall, unless they come with evidence that careful attention has been paid to the above
details.”
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Homonuclear Decoupling
The purpose of this section of the handout is to explain what homonuclear
decoupling does. Examples of a homonuclear decoupled spectrum are given in Figure 9.
Homonuclear decoupling is a double-resonance technique that uses two Rf fields to affect
magnetically active nuclei. Homonuclear decoupling involves applying a second RF field
to cause selective saturation of nucleus A while observing all other nuclei in the
Figure 9. Proton spectrum of 0.1% ethylbenzene in CDCl3 taken on a Varian Unity 400
MHz spectrometer. The lower trace is the full, coupled spectrum. The upper inset shows
that by centering the decoupler on the triplet the quartet is collapsed to a singlet, while
the lower inset demonstrates the effects of irradiating the quartet.
molecule; B, C, D, etc. If nucleus A is spin-coupled to nucleus B and if the second RF
field is strong enough, the result is that A is effectively prevented from spin-spin
interacting with B. The observed B nucleus spectrum will appear as if it is not coupled to
A. The A resonance commonly appears as a glitch (a.k.a. out of phase peak) as a result
of this experiment. As shown in Figure 9, if the triplet is homo-decoupled, the quartet
collapses to a singlet. Similarly, if the quartet is homo-decoupled, the triplet collapses to
a singlet. You may recall that a relatively high power, short Rf pulse will have a
frequency spread due to the Heisenberg Uncertainty Principle; therefore, the second Rf
field used for the selective decoupling will be lower power and have a longer duration.
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As a general rule-of-thumb, you will need a second Rf field that has a frequency that is
about 10 times larger than the coupling constant you are attempting to collapse. For
example, if you what to collapse a 15 Hz coupling constant, you will need a B1 field that
is about 150 Hz in magnitude. This is precisely why understanding how to convert a 90°
pulse width obtained at a particular value of tpwr, is essential to properly setting up a
double-resonance experiment. (Note: exactly the same requirement exists when setting
up a one-dimensional nOe experiment.) In this example, the soft irradiation on the single
signal would be at a value of tpwr corresponding to 1/150 Hz = ~6700 µs for the 360°
pulse-width, or about 1670 µs for the 90° pulse-width. Note: in practice to “deliver” this
much power will sometimes require a modest increase in the setting of the value of tpwr
(typically about +5 – +10 dB) because of the necessity of periodically interrupting the
irradiation when each data point is recorded during the FID (this interruption is called
“time-shared-decoupling”).
Homonuclear Decoupling Take Home Lesson
Homonuclear decoupling is a fast and effective way to establish that two nuclei
are spin (scalar, ‘J’) coupled, and can be used to simplify a complex coupling pattern for
further analysis. It is also useful as a follow-up to a COSY experiment to confirm specific
couplings. To obtain definitive data the two signals should be separated by at least 0.5
ppm. It is also important to note that other signals close to the irradiation point may
experience a displacement in their chemical shift due to the decoupling field. This
displacement in the chemical shift is called a Bloch-Siegert shift and can be used to
measure the decoupling field strength.
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1
H Decoupled 13C NMR spectra (13C-{1H})
The purpose of this section of the handout is to give you some useful information
about C-{1H} NMR spectroscopy. Since only about 1 in 100 carbon atoms are the NMR
active isotope (1.10% are the NMR active 13C), any means to improve S/N is essential.
Splitting of the 13C resonances as a result of coupling to attached hydrogen atoms will
result in decreased S/N and is, thus, undesirable. Therefore, 13C NMR spectra are
typically run 1H decoupled. The symbol 13C-{1H} is used to denote this and implies the
13
C nucleus is observed while the 1H nuclei are being irradiated, thus decoupling them
from the 13C nuclei. A typical 13C-{1H} spectrum (5% menthol in acetone-d6) is shown in
Figure 10.
13
Figure 10. A 13C-{1H} NMR spectrum of a 5% solution of menthol in acetone-d6
acquired on a Varian Unity 400 MHz spectrometer.
This is a double resonance experiment with the observed nucleus (13C) and
decoupled nucleus (1H) on separate Rf channels. This experiment is called heteronuclear
decoupling, and is another type of ‘1-PULSE’ experiment, as described in the Basics
section, with the addition of a decoupling field, as shown in Figure 11. It is the
heteronuclear version of the homodecoupling experiment with the exception that
broadband saturation (as opposed to selective saturation) is used.
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Figure 11. Representation of 13C-{1H}1-PULSE NMR experiment as presented on a
Varian INOVA 500 MHz Spectrometer. Note that the p 1 pulse is unused in this
sequence.
When acquiring spectra of nuclei other than 1H (so called ‘X- nuclei’) it is important to
remember the following considerations:
I. The Nuclear Overhauser Enhancement: The 13C-{1H} NMR spectrum
obtained using a standard 1-PULSE experiment is not quantitative, i.e., the
integration of the peaks will not give a true indication of relative ratios
because of a phenomenon called nuclear Overhauser enhancement (nOe)
arising from the continuous broad-band saturation of the hydrogen atoms.
13
C nuclei that have directly bonded hydrogen atoms can exhibit a signal
enhancement of up to 1.98 (198%), or an almost threefold improvement in
signal-to-noise. The nOe is from the dipolar through-space coupling of the
13
C and 1H nuclei and is dependent on many factors. Thus, the nOe will be
different for each unique carbon atom in a molecule. To obtain quantitative
13
C-{1H} spectra, you must do two things: follow the protocol given earlier
on integration, and carry out a ‘gated’ decoupling experiment, in which the
decoupler is gated on (turned on) ONLY during the acquisition time and
gated off (turned off) during the recycle delay. This is shown in Figure 12.
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Figure 12. A gated decoupling pulse sequence for 13C-{1H} acquisition that has no nOe
enhancement. Note that the decoupler channel (Dec) is only ‘on’ during segment C,
which is the pulse and acquisition time. Compare to Figure 11.
The result of this experiment is a 13C-{1H} spectrum without NOE and is
necessary for obtaining quantitative 13C spectra. SPECIAL NOTE: gated
decoupling typically requires an empirical increase in d1, to allow any nOe
that might begin to accumulate during the later part of at, to dissipate fully
before the next pulse.
II. T1 relaxation times: The Tl's of l3C nuclei are in general longer than those
found for hydrogen atoms, as shown below in Figure 13. Therefore, you
may have to wait very long times if you want accurate integrals from
spectra. For example, from Figure 13, quantitative integration of
ethylbenzene would require a total acquisition time (TT) of 5*36 seconds or
3 minutes per scan! A paramagnetic relaxation agent such as Cr(acac)
(available from Aldrich) can be used to shorten the Tl's, but can sometimes
be difficult to separate from the compound. Note that the quaternary carbon
atoms have considerably longer T1’s and, as a result, typically have much
smaller signals than other carbon atoms.
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14
7
CH2 -CH3
16
CH3
36
NO2
38
13
56
20
6.9
8.7
6.6
5.7
4.8
(CH3-CH2 -CH2-CH2 )2
9
6.9
21
13
15
13
4.9
Figure 13. Examples of some representative C NMR T1 values, in seconds.
13
C NMR Take Home Lesson
Obtaining useful 13C-{1H} spectra requires knowledge of the same basics as
needed for obtaining useful 1H spectra. When your spectrum doesn’t look right, you can
save frustration on the instrument be taking a quick spectrum of a 13C standard and
checking the S/N, or seeing if the standard is decoupled properly.
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13
C-{1H} DEPT Spectra
Distortionless Enhancement by Polarization Transfer (DEPT) is an experiment
that utilizes a polarization transfer from one nucleus to another, usually 1H to 13C or other
X nucleus, to increase the signal strength of the X nucleus. DEPT is an example of
multi-pulse, multi-channel experiment, which uses synchronous pulses on two channels
to afford polarization transfer. The pulse sequence is shown in Figure 14. In this case,
the decoupler channel (Dec) is 1H and the observe channel is 13C. Since we are
transferring the population difference of the hydrogen atoms to the X nucleus and gaining
signal intensity from these hydrogen atoms, it is the 1H T1’s that are important in
determining repetition
Figure 14. Schematic representation of a DEPT pulse sequence as displayed by a Varian
INOVA 500 MHz spectrometer. The observe (Tx) channel is 13C and the decoupler
(Dec) channel is 1H.
rate for a DEPT experiment. 1H T1’s can be significantly shorter than that of 13C and
especially short compared to 15N and 29Si, which allows you to acquire more scans per
unit time than the X-{1H} experiment and thus obtain improved S/N. A further
advantage of this population transfer is the ability to perform multiplicity editing.
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By varying the length of the last 1H pulse (mult*pp) from 45 to 135º degrees, the
multiplicity of the 13C or X nucleus can be determined (i.e. depending on the pulse, the
signal for a methine, methylene, or methyl carbon atoms will either be a positive,
negative, or null signal, see table below). Remember, since quaternary carbon atoms have
no attached hydrogen atoms, they will show no signal. Also, the signal from the
deuterated solvent will be absent. An example of a DEPT135 experiment is shown in
Figure 15. Compare it to Figure 10. In general, you can run DEPT on most samples
without additional calibration.
Figure 15. An example of a multiplicity-edited spectrum. Expansion of a 13C-{1H}
DEPT-135 spectrum of menthol taken on a Varian Unity 400 MHz spectrometer. The
relative sign of the peaks shows the multiplicity of the carbon atoms. The negative peaks
are methylene carbon atoms, while the positive peaks are either methyl or methine carbon
atoms (NOTE: quaternary carbon atoms are not detected).
If you obtain less than favorable results, calibration of the polarization pulse (pp on the
Decoupler channel) can be performed. This is typically done using a DEPT-90, arraying
pp, and looking for a maximum in the methine signal without contributions from other
carbon atoms.
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Pulse Angle (º)
45
90
135
Relative Intensities from DEPT
C (quaternary) CH (methine)
CH2 (methylene)
0
0.707
1
0
1
0
0
0.707
-1
CH3 (methyl)
1.06
0
1.06
DEPT Take Home Lesson
DEPT is an effective means of determining 13C multiplicity that, when combined with
other NMR spectra and other experimental techniques (MS, FT-IR, etc.), can be an
invaluable tool for the analysis of unknown compounds.
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